Jake DeBrusk scored on a breakaway for his first goal in 13 games, making it 3-0 at 14:01 of the second period.
"It's not just about scoring goals, it's about doing the little things right," Bergeron said. "And guys are doing that, and I think [DeBrusk is] one of them. And when you do that and you stay in position, you do the right things out there … most often than not, the puck's going to find you at some point and you get rewarded. So good for him to get that goal."
The Bruins outshot the Rangers 19-3 in the second period.
"You've got to take care of business and play to your strengths," Boston coach Bruce Cassidy said. "So obviously tonight we're a good defensive team. Want to make it hard on teams, get that message out there, which I'm sure it already is. But reinforce it, and I thought we did that."
Brandon Carlo scored off Shesterkin's skate from a sharp angle to make it 4-0 at 1:07 of the third period. Carlo, playing his second game after missing 18 with an upper-body injury, had 10 shot attempts, including five on goal.
"To see his confidence where it's at, he's a tremendous player and it means a lot to this group," McAvoy said of the defenseman. "So to have him back and see him playing well and being a big part of it is awesome."
NOTES: Rangers forward Pavel Buchnevich served a one-game suspension for high-sticking Capitals forward Anthony Mantha on Wednesday. Tim Gettinger replaced him and had two shots and four hits in 13:28 of ice time in his season debut. … Bergeron extended his point streak to five games (four goals, two assists).